It's three hours flying from NZ to Australia so a little bit further than "just off"
NZ has excellent skiing on both main islands.
The temperatures are a little cooler than Hawaii to be sure, it hardly hits 30°C in summer.
If you're into hunting, fishing, bungy jumping etc then NZ is for you
Australia has some excellent mountains down south too Thredbo ski field is supposedly awesome (I've never been there). the thing about Australia is the sheer size, from sub antarctic (Tasmania) to tropical (Darwin in the Northern Territory) is has everything, lush tropical rain forests to deserts inland, it is a truely remarkable place. (Talk to Lowndsey and cryman, they're born and bred aussies and will probably be able to give you a better idea of the place)